Question: The grades on a geometry midterm at Gardner Bullis are normally distributed with $\mu = 75$ and $\sigma = 4.0$. Emily earned a $66$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{66 - {75}}{{4.0}}} $ ${ z \approx -2.25}$ The z-score is $-2.25$. In other words, Emily's score was $2.25$ standard deviations below the mean.